New posts in incompleteness

What is "magic" about the combination of addition and multiplication in formal arithmetic?

logic incompleteness formal-proofs

PA├ ∃xP(x) but PA$\nvdash$ P(n) for any n?

first-order-logic incompleteness nonstandard-models

What's wrong with this "proof" that Gödel's first incompleteness theorem is wrong?

fake-proofs incompleteness

Why can't we prove consistency of ZFC like we can for PA?

logic set-theory model-theory incompleteness

Why bother with Mathematics, if Gödel's Incompleteness Theorem is true?

logic incompleteness meta-math

What does it mean for something to be true but not provable in peano arithmetic?

logic incompleteness

How can we know we're not accidentally talking about non-standard integers?

logic model-theory proof-theory turing-machines incompleteness

Examples of statements which are true but not provable

logic incompleteness

Are the Gödel's incompleteness theorems valid for both classical and intuitionistic logic?

logic proof-theory incompleteness

Is there a proof of Gödel's Incompleteness Theorem without self-referential statements?

logic incompleteness

Why is Gödel's Second Incompleteness Theorem important?

logic formal-languages proof-theory incompleteness

With this definition of completeness, Gödel's Incompleteness result seems not surprising, so why it was back then?

logic first-order-logic incompleteness

Are we sure Millenium Prize Problems can be solved?

logic incompleteness decidability

Statement provable for all parameters, but unprovable when quantified

logic incompleteness peano-axioms provability

How does Gödel Completeness fail in second-order logic?

logic model-theory first-order-logic incompleteness nonstandard-models

Could it be that Goldbach conjecture is undecidable?

number-theory logic incompleteness goldbachs-conjecture

Does Gödel's Incompleteness Theorem really say anything about the limitations of theoretical physics?

logic physics incompleteness

Is consistency an axiom of mathematics?

set-theory axioms foundations incompleteness

What is the prerequisite knowledge for learning Godel's incompleteness theorem

logic self-learning incompleteness

What axioms Gödel is using, if any?

logic axioms incompleteness